See, I think this is exactly why you are begging the question.
The word purpose has lots of usages, but the one that seems to be discussed here is some intrinsic purpose that an object or creature has for existing.
I can perform an action with a purpose, which is different to my (personal) purpose for being alive, which is different again for some intrinsic purpose for why I am here in the first place.
It's this last purpose that daseiner1 was referring to when they asked "what’s the purpose of an amoeba? or a mosquito? or a duck? or a chimpanzee?"
They are questioning if that kind of purpose even exists.
Your argument is:
Some things have more purpose than others.
Therefore purpose exists.
In this next response you get closer to defining what purpose is - "level of purpose exhibited by higher-complexity organisms" - but we haven't really established what that purpose is or what it means to have more purpose. At best you seem to be equating complexity of behaviour to level of purpose, but I see no reason why complex behaviour should imbue some kind of purpose; all usages of the word purpose imply intent of some kind, and there are many complex processes that have no intent.
I will say that complex animals seem to be more purposeful than simple creatures, but that just means that they perform actions with more intent than simpler creatures, not that they have some intrinsic purpose themselves.